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Let $R$ be a commutative Noetherian ring. There are several characterizations below of Gorenstein rings in terms of classical homological dimensions of their modules. In this paper we use Gorenstein dimensions (Gorenstein injective and Gorenstein flat dimension) to describe Gorenstein rings. It seems that these new invariants are more appropriate to this end, than classical ones. To do this, we force to prove that Cohen-Macaulay rings of finite Gorenstein injective dimension are Gorenstein. Moreover a characterization for Gorenstein injective (resp. Gorenstein flat) modules over Gorenstein rings will be given in terms of their Gorenstein flat (resp. Gorenstein injective) resolutions.
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